In this paper, we study such polyadic analog of an identity of a group as m-neutral sequence. In particular, we prove that all Post’s equivalence classes of the free covering group of any n-ary group [where \(n = k(m - 1) + 1\) and \(k\ge 1\)] defined by m-neutral sequences form the \((k + 1)\)-ary group, which is isomorphic to the n-ary subgroup of all identities of the n-ary group in the case when \(m = 2\).
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Gal’mak, A.M., Kovaleva, V.A. On Identities and m-Neutral Sequences of n-Ary Groups. Commun. Math. Stat. 4, 495–508 (2016). https://doi.org/10.1007/s40304-016-0097-y
- n-Ary group
- m-Neutral sequence
Mathematics Subject Classification